Thanks for posting.
Usually, in these type of situations I would first start taking a look at the database itself.
Let's verify the following:
--What is the behavior if the database is taken offline, opened in FileMaker Pro and a search is performed?
--Will other Server-hosted databases crash during searches?
--Will the database crash if searches are performed on all layouts or any layout in particular?
I would try taking the database offline and saving a compact copy or clone of the file. You can even try recovering the file although it is not recommended to continue using a recovered file. If other databases are ok or a brand new database is ok, then I would believe the issue lies with the database.
Let me know how it works out.